<p>
  In Black–Scholes, that volatility is assumed to be constant, it is not reasonable especially for some exotic options in which the option's payoff is based on the changing volatility. Therefore we introduced the two volatility models to capture the volatility skew. The first approach, local volatility, assumes that the volatility is a deterministic function of time and the underlying asset price. This function must be chosen as to match the observed market option prices. In another stochastic volatility models, the asset price and its volatility are both assumed to be random processes.
</p>
<p>
  The calibration needs the market price of the Vanilla options. When we get the model estimation we can use these models to price exotic options.
</p>
